Your RIR Rooster over New Hampshire hen are not sex links. You just crossed two red breeds.
Your black sex linked rooster is split for barring. That means he has one barred gene and one not-barred gene. He is also split for Extended Black and a base Red gene, I’ll guess Wheaten. Barred Rock should have silver but that’s not a given. So I’ll guess he is split for gold and silver.
Your black sex link hens only have not-barred but are also split for black and red. She got a gold from her father.
About half the chicks will be barred, half will not. That can be either sex. You can get a wide range of colors and patterns. Some you would expect. You might see some black and white barred like the rooster, some whitish without the barring, some black with no barring. You might see some red and some red barred. That red can be various shades from dark to kind of orangy. I once had a black rooster with a yellow neck and wings. That’s unlikely but possible. He looked nice. The males are normally more brightly colored than the females but you can still get some interesting colors and patterns. When you cross crosses like that you can get some surprises.
If you cross your BSL rooster over that red hen you’ll get pretty much the same colors and patterns but a lot more of them will be red instead of black.
If you cross your red rooster over the BSL hen you will get about half black and half red, no barring obviously but also no white. Those reds can be different shades of red.
Now for the disclaimers. On a lot of these you will get leakage. That’s where some random feathers come in red when the chicken should be solid black, for example. Different colors can leak and it is pretty random where and what will leak. Also other than the solid black or black barred chickens you should get a lot of black markings. Expect a lot of your red or white chicks to have black tails for example, maybe black on the necks or wings, especially on the roosters.
Donrae is right, you will get a rainbow of colors and patterns.
